访问类的所有函数中的全局变量

Is there a way that i can access $connect in all functions on class?

class topicClass {

    function viewTopic() {

        function grabId() {
         global $connection;

        }
        function grabTopic(){
            global $connection;

        }
        function grabReplies(){
            global $connection;
       }

    }

}

Instead of writing it over and over?

Define it as a property of your class, like so:

class topicClass {

   private $connection;

   public function __construct() {
      $this->connection = "myConnectionString";
   }

   function viewTopic() {
       // you can then refer to $this->connection here
   }
   ...
}

When you do:

var cls = new topicClass();

the construct() will be called and will assign the value to connection, and you can then refer to it in the other functions.

NOTE: In the example I gave, I used private. You may need to change that to public, depending on where you need to access it.